ALGEBRAIC PROPERTIES OF TOEPLITZ OPERATORS WITHSEPARATELY QUASIHOMOGENEOUS SYMBOLS ON THEBERGMAN SPACE OF THE UNIT BALL

摘要

In this paper we discuss some algebraic properties of Toeplitz op-erators with separately quasihomogeneous symbols (i.e., symbols being of the form kp(|z_1|...Z_n| )) on the Bergman space of the unit ball in C°. We provide a decomposition of L2 (B, dv), then we use it to show that the zero product of two Toeplitz operators has only a trivial solution if one of the symbols is separately quasihomogeneous and the other is arbitrary. Also, we describe the commutant of a Toeplitz operator whose symbol is radial.